The aim of this article is to articulate conceptually the varieties of international co-operation in which states take part. In theories of international relations, international co-operation is generally analysed either through instances of multilateral collaboration (EU, UN, NATO), through bilateral alliances (Franco-German relationship), or through “minilateral” clubs (G7). Yet the literature does not offer a concept for linking these three models of international co-operation. Nevertheless, in practice, states simultaneously use varieties of international co-operation to address global public problems such as climate change, migration crises, and the fight against terrorism. To address this shortcoming, it is necessary to shift the focus from each type of international co-operation to their “interstices”, in order to identify the relations between the types of international co-operation and their reciprocal effects on decisions taken by the state. It is to do this that the concept of “flexilateralism” has been developed. This neologism describes the policy through which a state simultaneously implements varieties of international co-operation to address a public problem. A state’s “flexilateral” policy, or flexilateralism, is operationalised by revealing four varieties of international co-operation: bilateralism (co-operation between two states), minilateralism (co-operation within an exclusive group of states), multilateralism (co-operation within an inclusive group of states), and unilateralism (no co-operation). The concept of flexilateralism is applied through the case of France’s defence procurement policy in the context of the Brexit negotiations. By taking seriously varieties of international co-operation, the concept of flexilateralism goes a step further to explain the policy-making and implementation of state’s foreign policy.